Neuter or to not neuter?

I have a spayed 7 year old female mini schnauzer at home for the past 2 years. She's a lovable, mellow love bug. I decided to get a companion for her recently, and I found a 4 year old un-nuetered male mini schnauzer that is a bit playful and a lot of fun. The 2 do not play much together since my female growls at him every time he gets too close and has the urge to mate with her. My question is, do I neuter my male dog in hopes that it'll calm his personality and not have the urge to mate with my female? I do not plan to breed for puppies or provide stud service.